TY - JOUR
T1 - An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion
AU - Samih Zein, Benoît Colson & François Glineur
JO - Communications in Computational Physics
VL - 4
SP - 1173
EP - 1188
PY - 2013
DA - 2013/08
SN - 13
DO - http://doi.org/10.4208/cicp.020911.200412a
UR - https://global-sci.org/intro/article_detail/cicp/7269.html
KW - 
AB - <p style="text-align: justify;">The polynomial chaos expansion (PCE) is an efficient numerical method for
performing a reliability analysis. It relates the output of a nonlinear system with the
uncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by using
a regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experiments
is large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of this
work is to propose an algorithm that generates efficiently a design of experiments of a
size defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experiments
in the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms of
accuracy and computational time reduction is compared with other existing methods
in the case of analytical functions and finite element based functions.</p>